%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET013-3 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:06:49 PM UTC 2026
% Result : Unsatisfiable 11.08s 7.31s
% Output : CNFRefutation 11.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 42 ( 11 unt; 8 nHn; 34 RR)
% Number of literals : 90 ( 14 equ; 41 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 57 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',intersection3) ).
cnf(intersection_of_b_and_a_is_d,hypothesis,
intersection(bs,as) = ds,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_of_b_and_a_is_d) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',intersection2) ).
cnf(intersection_of_a_and_b_is_c,hypothesis,
intersection(as,bs) = cs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_of_a_and_b_is_c) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',intersection1) ).
cnf(subset3,axiom,
( subset(X1,X2)
| ~ member(f17(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',subset3) ).
cnf(subset2,axiom,
( subset(X1,X2)
| member(f17(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',subset2) ).
cnf(extensionality3,axiom,
( X1 = X2
| ~ member(f1(X1,X2),X1)
| ~ member(f1(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',extensionality3) ).
cnf(subset1,axiom,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',subset1) ).
cnf(prove_c_equals_d,negated_conjecture,
cs != ds,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_equals_d) ).
cnf(extensionality2,axiom,
( member(f1(X1,X2),X1)
| member(f1(X1,X2),X2)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',extensionality2) ).
cnf(c_0_11,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_12,hypothesis,
intersection(bs,as) = ds,
intersection_of_b_and_a_is_d ).
cnf(c_0_13,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_14,hypothesis,
intersection(as,bs) = cs,
intersection_of_a_and_b_is_c ).
cnf(c_0_15,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_16,axiom,
( subset(X1,X2)
| ~ member(f17(X1,X2),X2) ),
subset3 ).
cnf(c_0_17,hypothesis,
( member(X1,ds)
| ~ member(X1,as)
| ~ member(X1,bs) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,hypothesis,
( member(X1,bs)
| ~ member(X1,cs) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,axiom,
( subset(X1,X2)
| member(f17(X1,X2),X1) ),
subset2 ).
cnf(c_0_20,hypothesis,
( member(X1,as)
| ~ member(X1,cs) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_21,hypothesis,
( subset(X1,ds)
| ~ member(f17(X1,ds),as)
| ~ member(f17(X1,ds),bs) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,hypothesis,
( subset(cs,X1)
| member(f17(cs,X1),bs) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,hypothesis,
( subset(cs,X1)
| member(f17(cs,X1),as) ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_24,axiom,
( X1 = X2
| ~ member(f1(X1,X2),X1)
| ~ member(f1(X1,X2),X2) ),
extensionality3 ).
cnf(c_0_25,axiom,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
subset1 ).
cnf(c_0_26,hypothesis,
subset(cs,ds),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_27,plain,
( X1 = intersection(X2,X3)
| ~ member(f1(X1,intersection(X2,X3)),X1)
| ~ member(f1(X1,intersection(X2,X3)),X3)
| ~ member(f1(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_11]) ).
cnf(c_0_28,hypothesis,
( member(X1,ds)
| ~ member(X1,cs) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,hypothesis,
( intersection(X1,X2) = ds
| ~ member(f1(ds,intersection(X1,X2)),cs)
| ~ member(f1(ds,intersection(X1,X2)),X2)
| ~ member(f1(ds,intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
cs != ds,
prove_c_equals_d ).
cnf(c_0_31,hypothesis,
( member(X1,as)
| ~ member(X1,ds) ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_32,axiom,
( member(f1(X1,X2),X1)
| member(f1(X1,X2),X2)
| X1 = X2 ),
extensionality2 ).
cnf(c_0_33,hypothesis,
~ member(f1(ds,cs),cs),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_14]),c_0_30]),c_0_20]),c_0_18]) ).
cnf(c_0_34,hypothesis,
( member(X1,cs)
| ~ member(X1,bs)
| ~ member(X1,as) ),
inference(spm,[status(thm)],[c_0_11,c_0_14]) ).
cnf(c_0_35,hypothesis,
( ds = X1
| member(f1(ds,X1),as)
| member(f1(ds,X1),X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,hypothesis,
( ~ member(f1(ds,cs),bs)
| ~ member(f1(ds,cs),as) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,hypothesis,
member(f1(ds,cs),as),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_35]),c_0_30]) ).
cnf(c_0_38,hypothesis,
( member(X1,bs)
| ~ member(X1,ds) ),
inference(spm,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_39,hypothesis,
( X1 = cs
| member(f1(X1,cs),bs)
| member(f1(X1,cs),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_32]) ).
cnf(c_0_40,hypothesis,
~ member(f1(ds,cs),bs),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).
cnf(c_0_41,hypothesis,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET013-3 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n001.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:04:49 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 11.08/7.31 % Version : CSE_E---1.7
% 11.08/7.31 % Problem : theBenchmark.p
% 11.08/7.31 % SZS status Unsatisfiable for theBenchmark.p
% 11.08/7.31 % SZS output start CNFRefutation
% See solution above
% 11.08/7.35 % Total time : 5.372s
%------------------------------------------------------------------------------